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전자정보대학 김영석 1 Stability and Frequency Compensation (Ch. 10) 김영석 충북대학교 전자정보대학 2010.3.1 Email: [email protected]

Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

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Page 1: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 1

Stability and Frequency Compensation (Ch. 10)

김 영 석

충북대학교 전자정보대학

2010.3.1

Email: [email protected]

Page 2: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 2

10.1 General Considerations

YX

(s) =H (s)

1+ βH (s)May oscillate at ω if |βH ( jω) |=1 and ∠βH ( jω) = −180 (Barkhausen criteria)

Basic Stability

Page 3: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 3

Stable and Unstable Systems(a) 위상=-180도에서 Excessive Gain>1 => Unstable

(b) 위상=-180도에서 Gain<1 => Stable

Page 4: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 4

Stability and Complex Poles(a) Unstable with Growing Amplitude

(b) Unstable with Constant Amplitude Oscillation

(c) Stable 0

0

0

<

=

>

p

p

p

σ

σ

σ

Page 5: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 5

Basic One Pole Bode Plot|βH|=1일 때 Phase -180도(Barkhausen 조건) 만족 못함

=> Unconditionally Stable

)1(1

1)(1

)()(

/1)(

00

0

0

0

0

AwsA

A

sHsHs

XY

wsA

sH

β

ββ

++

+=

+=

+=

Page 6: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 6

Multipole Systems

)/1)(/1()(

21

0

pp wswsA

sH++

=

|βH|=1일 때 Phase -180도에 근접하면 Unstable

Phase > -180도 => Stable

Page 7: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 7

Phase Margin

|βH|=1일 때 (Phase+180)=Phase Margin

Phase Margin ~ 0 => UnStable (a)

Page 8: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 8

Phase Margin (cont.)

Phase Margin, θm = 45°

Phase Margin=45도 이상이 필요함

Phase Margin=45도 일 때 주파수 overshoot 30%

Page 9: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 9

Phase Margin (cont.)

Phase Margin 증가하면 Time Domain Response 에서 Ringing 감소

(Freq Domain Response에서 Peaking 감소)

Page 10: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 10

Small Signal Analysis Limitations

Small signal analysis yields 65 ° of θm, but large signal transient response is different. Large signal simulation includes effects not

seen in small signal analysis.

다음 회로의 경우 Bode Plot(Small Signal Analysis)에서 PM=60도임. 그러나 Large Signal Analysis에서는 Ringing을 보임. 그 이유로 Slewing, 소자의 Nonlinear Behavior 때문임. Large Signal Application의 경우이와 같은 Time Domain 해석이 필요함

Page 11: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 11

10.4 Frequency Compensation

Compensation is the manipulation of gain and/or pole positions to improve phase margin.

Unstable System을 Stable하게 하기 위해서 Freq. Comp. 필요함

Page 12: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 12

Compensation (cont.)

Dominant Pole을 Low Freq 로 옮김 => PM 확보

Page 13: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 13

Single Ended Single Stage Amp

Dominant Pole=Wout: Large CL/Rout

A Node: Large Stray Cap. =>

2nd Dominant Pole

Page 14: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 14

Single Ended Single Stage Amp (cont)

Pre- and Post-Compensation

PM 없음 => Unstable

Freq Comp: Dominant Output Pole을 낮은 주파수로 이동 시킴. 다른 Pole 들은 그대로 둠. => PM 45도 확보

Page 15: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 15

Fully Differential Telescopic Op-AmpNo Mirror Pole => Bandwidth 증가

Page 16: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 16

10.5 Comp. of Two Stage Op AMpsWp,x: 높은 주파수

Wp,E: Large R => 낮은 주파수

Wp,A: R=ro, Large CL=> 낮은 주파수

Unstable

Page 17: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 17

Compensation (cont.)

Miller Effect Ceq = CE + (1+ Av2)CC

f pE =1

2πRout[CE + (1+ Av2)CC ]

Miller Compensation

Miller Cap Cc로 E Node의 Dominant Pole을낮은 주파수로 이동

Page 18: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 18

Compensation (cont.)

f p,in =1

2π RS CE + (1+ gmRL )CC[ ]+ RL (CC + CL)( )

Recall, from Chap. 6:(assume CC includes CGD9)

f p,in ≈1

2πRS CE + (1+ gmRL )CC[ ]

fp,in = Wp,E/2/pi => 작아짐

Page 19: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 19

Compensation (cont.)

f p,out ≈RSgm 9RLCC + RLCC

2πRS RL(CECC + CCCL )=

gm 9

2π (CE + CL )

f p,out =RS (1+ gm 9RL )CC + RSCE + RL(CC + CL)

2πRS RL(CECC + CECL + CC CL)

fp,out = Wp,A/2/pi => 커짐

Page 20: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 20

Compensation (cont.)

Recall, transfer function includes(1− s /ωz ) numerator term and

fZ(RHP) = gm9

2πCC

앞의 Compensation은 RHP zero 발생 => Phase margin 악화시킴

Page 21: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 21

Phase and Magnitude of RHP Zero

Page 22: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 22

RHP Zero Removal

fZ =gm 9

2πCC (1/gm 9 − RZ )

RHP zero 제거 위해 Rz 저항 삽입

Page 23: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 23

RHP Zero Removal (cont.)

fZ = 12πCC (1/ gm 9 − RZ )

Could set R z =1/gm9, or cancel other non - dominant pole

1CC (1/gm 9 − RZ )

= −gm9

CL + CE

RZ =CL + CE + CC

gm 9CC

≈ CL + CC

gm 9CC

= wp,A

Page 24: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 24

Miller Compensation (cont.)

Temp. and Process Tracking

on)Cancellati Zero(Pole

조절 I 되게 1

−+=

=

=

=

)1(1

)/()/(1

)/(1

9

15

14

14151515

1415

913

C

L

m

moxpon

GSGS

GSGS

CC

g

LWLW

gVLWCR

VVVV

μ

Page 25: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 25

Miller Compensation (cont.)Defining gm9 with respect to Rs

Page 26: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 26

Load Capacitance EffectsOne Stage: Increase CL => Increase PM => More Stable

Two Stage: Increase CL => Output Pole을 낮은 주파수로 이동 시킴. Cc에 의한 1st Stage Output Pole(Dominant)쯕으로 이동시켜 PM을 악화시킴

Page 27: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 27

10.6 Other Compensation Techniques

Page 28: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 28

Other Compensation Techniques (cont.)

f p1 ≈1

2πRS gm1RLCC

f p2 ≈gm1

2πCL

Page 29: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 29

Other Compensation Techniques (cont.)

Page 30: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 30

Other Compensation Techniques (cont.)

f p1 ≈1

2πRS gm1RLCC

f p2 ≈gm1gm 2RS

2πCL

Page 31: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 31

Slewing in Two-Stage Op Amps

Basic Two-Stage Op Amp

Page 32: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 32

Slewing in Two-Stage Op Amp

Page 33: Stability and Frequency Compensation (Ch. 10)bandi.chungbuk.ac.kr/~ysk/ana10.pdf · ∠βH(jω) =−180 (Barkhausen criteria) Basic Stability. 전자정보대학김영석 3 Stable

전자정보대학 김영석 33

Slewing with Common-Gate Compensation